Groupoid Approach to Quantum Projective Spaces

We show how the C*-algebras of quantum complex projective spaces (standard or nonstandard) are related to groupoids.Comment: 12 page

The Structure of Line Bundles over Quantum Teardrops

Over the quantum weighted 1-dimensional complex projective spaces, called quantum teardrops, the quantum line bundles associated with the quantum principal U(1)-bundles introduced and studied by Brzezinski and Fairfax are explicitly identified among the finitely generated projective modules which are classified up to isomorphism. The quantum lens space in which these quantum line bundles are embedded is realized as a concrete groupoid C*-algebra

Assessing Complementarities Among Farm Machineries Through Farmers' Investment Behaviors Under An External Capital Injection – Implications on Agricultural Mechanization and Tractorization In Sub-Saharan Africa

Agricultural Finance, Farm Management,

S-Lemma with Equality and Its Applications

Let $f(x)=x^TAx+2a^Tx+c$ and $h(x)=x^TBx+2b^Tx+d$ be two quadratic functions having symmetric matrices $A$ and $B$. The S-lemma with equality asks when the unsolvability of the system $f(x)<0, h(x)=0$ implies the existence of a real number $\mu$ such that $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$. The problem is much harder than the inequality version which asserts that, under Slater condition, $f(x)<0, h(x)\le0$ is unsolvable if and only if $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$ for some $\mu\ge0$. In this paper, we show that the S-lemma with equality does not hold only when the matrix $A$ has exactly one negative eigenvalue and $h(x)$ is a non-constant linear function ($B=0, b\not=0$). As an application, we can globally solve $\inf\{f(x)\vert h(x)=0\}$ as well as the two-sided generalized trust region subproblem $\inf\{f(x)\vert l\le h(x)\le u\}$ without any condition. Moreover, the convexity of the joint numerical range $\{(f(x), h_1(x),\ldots, h_p(x)):~x\in\Bbb R^n\}$ where $f$ is a (possibly non-convex) quadratic function and $h_1(x),\ldots,h_p(x)$ are affine functions can be characterized using the newly developed S-lemma with equality.Comment: 34 page

Response to Comment on “Characterization of Excess Electrons in Water-Cluster Anions by Quantum Simulations”

In response to the Comment by Neumark and co-workers, we reiterate that the conclusions of the title Report are based on identifiable characteristic trends in several observables with cluster size. The numerical comparison between simulated and experimental vertical detachment energies emphasized in the Comment reflect quantitative limitations of our atomistic model, but, in our opinion, do not undermine these conclusions

Nigerian Farmers' Preferences On Specific Timing and Channel for Cereals and Legume Seeds Delivery–An Empirical Estimation of Willingness to Pay (WTP) through Mixed Preference Models

Crop Production/Industries, Farm Management,